Quantum Gravity and String Theory

Lanczos-Lovelock and f ( R ) Gravity from Clifford space Geometry

A rigorous construction of Clifford-space Gravity is presented which is compatible with
the Clifford algebraic structure and permits the derivation of the generalized connections
in Clifford spaces ( C-space) in terms of derivatives of the C-space metric.
We continue by arguing how Lanczos-Lovelock higher curvature gravity can be embedded into
gravity in Clifford spaces and suggest how this might also occur for extended gravitational theories based on f ( R ),
f ( R_{\mu \nu} ), .... actions, for polynomial-valued functions. Black-strings and
black-brane metric solutions in higher dimensions D > 4 play an important role in finding specific examples.

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